Our bass relaxing in private (3,4)
I believe the answer is:
sub rosa
'private' is the definition.
(thesaurus)
'our bass relaxing' is the wordplay.
'relaxing' is an anagram indicator.
'our'+'bass'='ourbass'
'ourbass' is an anagram of 'SUB-ROSA'.
'in' acts as a link.
(Other definitions for sub rosa that I've seen before include "In strict confidence - in Latin" , "Confidential in floral way" , "Behind closed doors" , "Secretly" , "In confidence, beneath nice flower" .)